Download Combinatorial Circuits

Ch3. Combinatorial Logic Design
Modern digital design involves a number of
techniques and tools essential to the design of
complex circuits and systems. In this chapter we
will learn about the design of combinatorial circuits.
Topics include
• Design Hierarchy
• Top-Down Design
• CAD tools
• HDL
• Logic Synthesis
CMPT150, Ch 3, Tariq Nuruddin,
Fall 06, SFU
1
Logic Circuits
These can be Sequential or Combinatorial.
In Sequential Circuits the output, o(t) which is time dependent
can take a value using the input at any time, t or prior to t.
In Combinatorial Circuits the output, o(t) depends on the value
of the input at the current time, t only. The parameters for
optimizing combinatorial circuits are
• Logic Gates
• Boolean expressions
• Input variables
• Output variables
• Interconnections
CMPT150, Ch 3, Tariq Nuruddin,
Fall 06, SFU
2
Behavioral Description
As mentioned earlier, a behavioral description specifies what a
circuit does, but not how. Behavioral descriptions ALWAYS
consist of two parts:
• An entity definition that identifies the signal lines that make
up the inputs and outputs and the ports that interface the device
with those signal lines. A signal line is any connection that can
transmit one bit at a time. An entity can be referred to as a
module consisting of specific tasks.
• A functional specification that specifies how the outputs are
determined by the inputs. For an n-variable binary function,
there are 2n input sequences and a maximum of 2# of input sequences
possible output combinations.
CMPT150, Ch 3, Tariq Nuruddin,
Fall 06, SFU
3
Relationship: Specifying and Implementing
If some requirement is specified, then it must be
designed. If it can be designed can we implement the
idea behind it? If so, what is the most optimal strategy?
Specification:
What
Design
Analysis
Implementation:
HOW
CMPT150, Ch 3, Tariq Nuruddin,
Fall 06, SFU
4
System Specification: WHAT
• It is a functional or behavioral description of the
system function
• Describes requirements/characteristics for its use. It
could be in the form of English descriptions, entity
definition, function tables, algebraic expressions, state
diagrams, hardware description languages, etc.
• Should be complete (output for every input)
• As simple as possible
• Unambiguous: unique output given an input
sequence
• No irrelevant details
CMPT150, Ch 3, Tariq Nuruddin,
Fall 06, SFU
5
System Implementation: HOW
Describes how simpler modules are interconnected to
implement the system. (Also referred to as structural
description).
The modules can be:
• electronic gates,
• logic gates,
• integrated circuits or
• whole processors.
CMPT150, Ch 3, Tariq Nuruddin,
Fall 06, SFU
6
Design Hierarchy
This uses a divide-and-conquer approach in building complex
integrated circuits. It involves usage of block diagrams to
represent circuits. Figure 3-2 (a) on page 90 of text shows a 9input odd function circuit.
X0
This circuit can be
broken into smaller
pieces or blocks. The
schema for the other
blocks are shown on
page 90.
X1
X2
X3
X4
X5
9-Input
odd
function
X6
X7
Z0
X8
CMPT150, Ch 3, Tariq Nuruddin,
Fall 06, SFU
7
Hierarchical Diagram for the 9-input odd function
The detailed diagram
of the 9-input odd
function is shown on
page 91 of the text.
The total number of
ways to complete a
9-input odd function
is
1  4  2  4 = 32
Step 1 can be
represented in
only one way.
Step 2 can be
completed in
4 ways.
9-input odd function
3-input odd function
Step 3 can be
completed in
2 ways.
Step 4 can be
completed in
4 ways.
CMPT150, Ch 3, Tariq Nuruddin,
Fall 06, SFU
XOR
N
A
N
D
8
Top Down Design
This top down design
concept is analogous
from General-to-Specific
of from Specific-toGeneral in Database
Management Systems.
The application requires
text description,
optimization, cost,
performance, reliability,
etc. The optimization
process may include
constraints in order to
have a parsimonious
structure.
System
Top
Modules
Gates, entities, etc
Bottom
Transistors,
Contemporary
Circuits
CMPT150, Ch 3, Tariq Nuruddin,
Fall 06, SFU
9
CAD
Computer-aided-design uses blocks or functional blocks,
libraries of graphic symbols to design integrated circuits.
After completion the verification of outputs within a design
is performed using a logic simulator. Optimization of
designs is performed using a logic simulator.
CMPT150, Ch 3, Tariq Nuruddin,
Fall 06, SFU
10
Hardware Description Language, HDL
HDLs provide an alternative to schematics. HDLs have a
structural description, i.e., they provides an interconnection to
components. Such a structural description , i.e., which
provides an interconnection to components (Netlist). A Netlist
can be used as an input to logic simulation just as a schematic is
used. HDL can be used to represent boolean equations, truth
tables, arithmetical operations, etc. HDLs can be used at an
intermediate level (RTL ). Register Transfer Languages, RTLs
use a library of components to convert a description into an
interconnection of primitive components that implement the
circuit. Two very popular HDLs are VHDL and VERILOG.
CMPT150, Ch 3, Tariq Nuruddin,
Fall 06, SFU
11
Logic Synthesis
HDL Description
of Circuit
Electronic, Speed,
and Area Constraints
Technology
Library
Translation
Intermediate
Representation
Preoptimization
Optimization
Technology Mapping
Netlist
CMPT150, Ch 3, Tariq Nuruddin,
Fall 06, SFU
12
Design Space
Any given design can be implemented using the design properties
and available technology. A set of constraints (conditions) are
applied during the implementation process. They are as follows:
• Gate Properties
• Levels of Integration
• Circuit Technologies
• Technology Parameters
• Positive and Negative Logic
• Design Trade-Offs
A few of these constraints are discussed in the next set of slides.
CMPT150, Ch 3, Tariq Nuruddin,
Fall 06, SFU
13
Levels of Integration
Digital systems are constructed from components that have varying degrees of
complexity. So far only the simplest digital components have been used, namely
gates. Components can be classified broadly into four groups based on the "gate
equivalency" of the digital components on the chip. Gate equivalency refers to the
estimated number of gates that would be required to construct the digital system
using discrete gates as the only components. Digital components are classified
according to their gate equivalency:
• SSI (Small Scale Integration) refers to chips that have from 1 to 10 gates
fabricated on their silicon substrates. Thus a single chip may have 6 inverters, 3 or 4
AND gates, or 1 or 2 OR gates depending on the number of inputs.
• MSI (Medium Scale Integration) refers to chips that have a gate equivalency of
10 to 100 gates per chip. This includes components such as adders, multiplexers,
decoders, flip-flops, and registers.
• LSI (Large Scale Integration) includes components that have a gate equivalency
of 500 to 5000 gates per chip, and includes devices such as arithmetic logic units
(ALUs), read-only-memories (ROMs), and register files.
• VLSI (Very Large Scale Integration) includes components that have more than
10,000 gates/chip.
CMPT150, Ch 3, Tariq Nuruddin,
Fall 06, SFU
14
Circuit Technologies
The factors involved in circuit technology are high
circuit density, high performance, low power
consumption, etc. Currently CMOS, Complementary
Metal Oxide Semiconductor technology is widely
used. A few other types discussed in class are
PMOS, VMOS, etc.
CMPT150, Ch 3, Tariq Nuruddin,
Fall 06, SFU
15
Technology Parameters
The most important parameters used to characterize and
implementation technology are as follows:
• Fan-in specifies the number of inputs available on a gate.
• Fan-out specifies the number of standard loads driven by a
gate output.
• Noise margin is the maximum allowable noise
superimposed on a normal input value.
• Propagation delay is the time required for a change in
value of a signal to propagate from input to output.
• Power dissipation is the power drawn from the power
supply and consumed by the gate. This is dissipated as heat.
CMPT150, Ch 3, Tariq Nuruddin,
Fall 06, SFU
16
Positive and Negative Logic
If we use a “0” or “1” logic state at the input or output levels, then
the “1” logic level could be representing 5V or perhaps some other
value. The “0” logic level could be representing 0V or perhaps
some other value. The operation could be defined as positive logic
and negative logic. This depends on how we select to
voltage/current to indicate the “0” and “1” binary values. Positive
logic occurs when the “1” logic level has a more positive value than
the “0” logic level. Negative logic occurs when the “0” logic level
has a more negative value than the “1” logic level.
5V
‘1’ logic level
3V
t
0V
‘0’ logic level
‘1’ logic level
t
0V
-7V
‘0’ logic level
CMPT150, Ch 3, Tariq Nuruddin,
Fall 06, SFU
17
Design Trade-Offs
How can we decide on the
design? Consider the
diagram shown here.
Increasing the Fan-outs can
increase the propagation
delay, and perhaps cause
overheating. Adding a buffer
at F can reduce propagation
delay whereby increasing the
cost value? Look up possible
circuit constraints on page
104 of text.
Two Fan-ins
A
F
Gate 1
CMPT150, Ch 3, Tariq Nuruddin,
Fall 06, SFU
B
Three Fan-outs
Gate 2
Gate 3
G
18
Design Procedure
The following steps are involved in this procedure:
• Specification (specification or requirement for the circuit)
• Formulation (truth tables, boolean expressions between I/O)
• Optimization (two-level or multiple level)
• Technology Mapping (transforming the logic diagram or netlist
to new diagram or providing a netlist for the resulting circuit using
primitive gates)
• Verification (verify the correctness of the final design)
Look up example on page 105 of text
CMPT150, Ch 3, Tariq Nuruddin,
Fall 06, SFU
19
Programmable Implementation Technologies
A programming logic device may have hundreds to millions
of gates. The common types of programming logic devices
are:
• ROM
• Programmable array logic (PAL)
• Programmable logic array (PLA)
These are discussed on pages 126 to 132 of the text.
CMPT150, Ch 3, Tariq Nuruddin,
Fall 06, SFU
20